Degeneracy in the Fraunhofer diffraction of truncated Gaussian beams

The variations of the Fraunhofer diffraction pattern formed by a Gaussian beam passing through a circular aperture are described. It is shown that a discontinuous process of several steps occurs as the beam truncation by the aperture decreases. Each step consists of a sequence of mergers of two neighboring diffraction rings. This sequence repeats continuously and finally leads to the degeneration of the Airy pattern into a single spot, i.e., the Gaussian pattern corresponding to the Fraunhofer diffraction of a nontruncated Gaussian beam.